TBH, I didn't intend that particular idea to serve as a power source - just explaining what "700kg of energy" is. About 63000 petajoules, or 4*10
38 electronovolts, or 6.3*10
26 ergs, or even 6*10
16 BTU. Whatever. A tremendous amount of energy, but it doesn't seem impossible. Now, we go find some good fusion fuel. According to AtomicRockets, D+He3 gives us 353.23 TJ/Kg. Now it's a rather trivial division to find we'll need about 180T of fusion fuel, assuming we can reclaim 100% energy produced (or that AtomicRocket counted in the loss in it's figure). That's a lot, but there's much more water on Earth than that. He3 could be a problem, if you want to propose a different fuel mix, just give me the numbers for it (gotta love Mathematica, once you come up with a routine, you can run it for any good data).

Now the question boils down to two factors: making fusion power work and lifting 180T or something of fuel into space. Soviets could've had the capacity to do the latter by the 90s (proposed Energia-Vulkan booster could probably make that much to LEO) if it wasn't for politics, so could US with the Nova rocket. The former is being researched and we're making good progress. So we could probably power the thing by fusion just fine.
Now, could we afford this? Nope, not today. But someday it might change. It's definitely not physically impossible, even with 10 times less efficient fusion reaction (D-T, for example), it boils down to an engineering problem, and one that can be solved "brute force" by building more superheavy LVs. Also, 700kg is for an FTL version, I imagine that the STL one would be much cheaper in terms of energy.
I think that discussing engineering details of a car before the idea of a wheel has been fully proven is somewhat far-fetched, but if White's research is enough of a proof for you, we can talk that, sure.

But IMO, it's a whole different discussion.
One nice thing is, I noticed one problem with the concept thanks to this discussion. Assuming it's an actual proposal, there's no way it could run on fusion, there's not enough space for fuel tanks. 180T of light elements, even if you liquefy them, takes a lot of space. Now, Star Trek ships are A-M powered, but as you highlighted, I'd rather take my chances with 72T of deuterium and 108T of He3, and building an efficient fusion reactor.
